Higher level and more difficult quests grant more experience (you can also invest in the inn 3 times (more than that is basically a waste of gold) to speed up the quest).

You can also invest gold directly into hero buildings to level heroes. Each hero gets experience from specific buildings (for example, Theor and Gauvin get experience by investing in the training hall) which can be found by clicking on an icon directly below the hero's level on their hero card.

Sometimes words might not be enough to drive the point in. Retep is correct, but I want to show you why, and by how much.

Inn Boosting brings your Quest time down to the minimum 15% of the original quest time. When your Inn is reducing by 50% (max level), this only takes 3 boosts. When your Inn is reducing by less, it may take up to 6, 7, or 8 boosts to hit the capped 15%. This amount can be reduced further with other effects like Boosting the Inn for the up-front time reduction, and with Hero / Item Skills Speed Runner. By boosting, you get 6.66 times more experience, per minute, than you would without Inn Boosting. By completing quests faster, you are going to get to the boss fights faster. When you get to the boss fights, you raise the amount of experience you get and the number of artifacts you find.

You can make this even better by getting your heroes with Energetic and Healer skills to reduce resting time so you can quickly re-launch quests.